Vrachier 8000 TDW

Vrachier 8000 TDW

MAXIM CRISTIAN CONSTANTIN

CUPRINS1CUPRINS

CAPITOLUL 1 3DOCUMENTARE

CAPITOLUL 2 6DESCRIEREA GENERALA A NAVEI

72.1 CARACTERISTICILE NAVEI

72.2 DIMENSIUNI PRINCIPALE

72. 3 CLASA NAVEI

82.4 DEADWEIGHT

82.5 VITEZA

82.6 MOTOR PRINCIPAL

82.7 AUTONOMIE

92.8 STRUCTURA ECHIPAJULUI

92.9 STABILITATE I ASIET

92.10 COMPARTIMENTAREA NAVEI

92.11 MATERIALE

92.12 INSTALAIILE NAVEI

CAPITOLUL 3 11DETERMINAREA DIMENSIUNILOR PRINCIPALE SI A COEFICIENTILOR DE FINETE

123.1 CALCULUL DEPLASAMENTULUI NAVEI CUNOASCND DEADWEIGHT-UL

123.2 LUNGIMEA NAVEI

143.3 LIMEA NAVEI

143.4 PESCAJUL NAVEI

153.5 INLIMEA DE CONSTRUCIE

163.6 COEFICIENI DE FINEE

CAPITOLUL 4 19FORMELE NAVEI

204.1 GENERAREA PLANULUI DE FORME UTILIZND PROGRAMUL MULTISURF

214.2 TABELUL DE TRASAJ PE CUPLE

CAPITOLUL 5 28CALCULE HIDROSTATICE PE PLUTIRI DREPTE

295.1 CALCULUL HIDROSTATIC PE PLUTIRI

615.2 CARACTERISTICI DE VOLUM

635.3 COEFICIENTI DE FINEE

645.4 TRASAREA DIAGRAMEI DE CARENE DREPTE

CAPITOLUL 6 65DETERMINAREA DEPLASAMENTULUI NAVEI GOALE, DEADWEIGHT-ULUI SI A REZERVELOR

666.1 CLASIFICAREA GRUPELOR DE MASE

666.2 DETERMINAREA GRUPELOR DE MASE PRIN METODA PARSONS

CAPITOLUL 7 70CALCULUL REZISTENTEI LA INAINTARE SI A PROPULSIEI

717.1 .CALCULUL REZISTENEI LA NAINTARE

757.2 ESTIMAREA PRELIMINAR A PROPULSIEI I ALEGEREA MOTORULUI

777.3 PROIECTAREA ELICEI

CAPITOLUL 8 82ESANTIONAJUL NAVEI IN ZONA CENTRALA

838.1 EANTIONAJUL NAVEI N ZONA CENTRAL

838.2 GROSIMI MINIME

898.3 ELEMENTE DE OSATUR N AFARA TANCURILOR DE GURN I DE ANTIRULIU

928.4 TANCUL DE GURN [PARAGRAF 23, B.4.4] + [PARAGRAF 8, B.4]

978.5 TANCURI ANTIRULIU [PARAGRAF 23, B.6]

CAPITOLUL 9 104EVALUAREA STABILITATII INITIALE IN CAZURI TIPICE DE INCARCARE

1059.1 CALCULAREA GRUPELOR DE MASE

1059.2 CALCULUL DIFERITELOR SITUAII DE NCRCARE ALE NAVEI

CAPITOLUL 10 106PROIECTAREA INSTALATIEI DE SANTINA

10710.1 INSTALAIA DE SANTIN

10710.2 ELEMENTE COMPONENTE ALE INSTALATIEI DE SANTINA

10810.3 SCHEME FUNCTIONALE ALE INSTALATIILOR DE SANTINA

10910.4 CALCULUL INSTALATIEI

11210.5 SCHEMA FUNCIONAL A INSTALAIEI DE SANTIN (VEDERE DEASUPRA DUBLULUI FUND)

CAPITOLUL 11 TEMA SPECIALA 113DIMENSIONAREA OPTIMA A PLANSEULUI DE DUBLU FUND

11411.1 FUNDAMENTE TEORETICE

12011.2 MODEL DE CALCUL

12111.3 UTILIZAREA ADD-IN-ULUI SOLVER DIN EXCEL PENTRU REZOLVAREA PROBLEMEI DE OPTIM

12411.4 VERIFICAREA STRUCTURII REZULTATE PRIN METODA ELEMENTULUI FINIT

13411.5 CONCLUZII

Bibliografie135

CAPITOLUL 1

DOCUMENTARE

n urma unei documentri am ales un numr de 17 de nave construite n ultimii 25 de ani, cu dimensiuni i caracteristici apropiate de cele ale navei de proiectat. Pe baze statistice putem determina dimensiunile principale, deadwight-ul, puterea instalat, turatia motorului etc. Toate rezultatele obinute sunt consultative urmnd s trecem la proiectarea propriu-zis.

Caracteristicile acestor nave sunt prezentate n tabelele de mai jos.

Nr. navaNumeSteagDwtLOALPPBDTViteza

01234567810

1SumatraItalia7800.00107.00102.8816.309.757.5010.00

2Sider SunMalta7376.00119.60115.4416.808.206.3012.00

3Marine KobePanama6485.00109.05105.8716.448.766.7411.00

4Coreea de sud6036.00108.45105.2916.409.156.6014.00

5SecaPanama8746.00100.3393.5019.6013.008.2613.80

6Sider TideItalia6280.00111.30108.0618.007.555.8111.00

7TbnPanama6500.00100.8097.8617.209.006.8313.00

8Bulk9000.00108.00104.8518.009.507.6012.00

9Badger IIFilipine7353.00100.7097.7718.309.357.4312.00

10Turcia7051.0097.8089.0117.019.207.4614.00

11Hai MenSt. Vincent8036.00109.58102.0018.309.357.2513.00

12WygosSpania9062.00120.00116.5018.5510.008.3713.00

13Timber StonePolonia7850.00131.60122.0017.008.807.0013.00

14Permai IISingapore7652.00120.53111.9917.848.826.5013.00

15B-HartPanama9413.00115.30105.7019.0010.508.1313.00

16Atasoylar IITurcia8379.00115.95106.8017.209.807.5812.00

17Dim9062.00120.00110.0018.5510.008.3713.00

Nr. navaNumeAn fabricatieMotor principalPutereaRPMClasa

01911121316

1Sumatra1987PIELSTICK2200 KWRINA 100 A1

2Sider Sun2005DAIHATSU 8DKM-282500 KW750 RPMNK NS* MNS*

3Marine Kobe1982MITSUBISHI 6UEC37/88H3900 CPKR CLASS

41996FUJI DIESEL2600 KW330 RPMKR CLASS

5Seca1997KAWASAKI MAN B&W 6L35MC5280 CP1200 RPMNK NS* MNS*

6Sider Tide1992HANSIN DIESEL WORKS3500 CPBV CLASS

7Tbn1998AKASAKA MHI 6UEC3800 CPNK NS* MNS*

8Bulk2006WARTSILA 6L322740KW750 RPMCCS CLASS

9Badger II1997AKASAKA4400 CPNK NS* MNS*

101983MAK 8M452AK 32641 CPABS CLASS

11Hai Men1991HITACHI 6L35MC4101 CPCCS CLASS

12Wygos1984MAN8L40/54A3680 KW450 RPMKR CLASS

13Timber Stone1989B&W 7L45GBE6376 CPRS-ICE STRENGTHENED-1A

14Permai II1980MITSUBISHI 6UET45/80D2941 KWGL 1C

15B-Hart1985MAKITA-MITSUI-B&W 6L35MC4080 CP200 RPMKR CLASS

16Atasoylar II1991WARTSILA, 9R32D4585 CP750 RPMBV CLASS

17Dim1984MAN 8L40/54A5000 CP450 RPMGL 1C

CAPITOLUL 2

DESCRIEREA GENERALA A NAVEI

Prezenta descriere are ca scop s prezinte ct mai complet construcia corpului, suprastructura, mainile, accesoriile i performanele vrachierului de 8000 tdw.

2.1 CARACTERISTICILE NAVEI

Nava este de tip vrachier destinat s transporte mrfuri generale, crbune, minereu de fier, fosfai, grne i cherestea.

Nava care este propulsat de un motor principal lent, are o singur punte continu, suprastructur, bulb la prova.

Nava are 3 magazii, amenajate s transporte mrfuri uscate, minereu, crbune, fosfai i gru. Dublu fund este extins ntre pereii picurilor, C.M. amplasat n pupa navei i sub toate magaziile.

Nava nu este prevzut cu perei longitudinali, are tancuri superioare amplasate n borduri, sub puntea principal, ntre compartimentul maini i picul prova.

Tancurile de combustibil sunt amplasate n zona magaziilor n dublul fund precum i n zona compartimentului de maini.

Tancurile de balast sunt amplasate n picurile pupa i prova, n tancurile superioare i n dublul fund ( n zona magaziilor).

2.2 DIMENSIUNI PRINCIPALE

LWL - lungimea la linia de plutire

122 m

LPP - lungimea ntre perpendiculare

119 m

B - limea navei

16,8 m

T - pescajul navei

6,8 m

D - nlimea de construcie

9,52 m

Deadweight

8000 tdw

2. 3 CLASA NAVEI

n conformitate cu Regulile pentru Clasificarea i Construcia Navelor Maritime ale Registrului Germanisher Lloyd clasa navei va fi:

100 A5 BULK CARRIER (single side skin)

MC - 100A5 Corpul navei corespunde cerinelor Regulilor de Constructie ale Germanisher Lloyd

- BULK CARRIER - Tipul navei - MC Instalaiile inclusiv instalaiile electrice corespund cerinelor Regulilor de Constructie ale Germanisher Lloyd

Nava va trebui s respecte urmtoarele Reguli i Regulamente inclusiv protocoalele i amendamentele n vigoare.

1. Cargo stowage and securing;2. International Load Line Convention;

3. International Convention on Tonnage Measurement of Ships;

4. MARPOL 73/78 2002 Consolidated edition;

5. SOLAS 2001 Consolidated edition;

6. International Telecommunications and Radio Regulations, including

GMDSS 1989 / 1990;

7. Suez Canal Rules including Tonnage Measurements;

8. Safe loading and unloading of bulk carriers;

9. GL Rules regarding marine pollution as applicable to foreign flag vessels;

10. IMO resolution as applicable at this type of ship, request by Class.

2.4 DEADWEIGHT

Deadweight-ul navei complet dotat, gata de exploatare i cu marf , n ap de mare (greutatea specific 1,025 t/m3) la pescajul de eantionaj de 6,8 m, pe chil plat este de aproximativ 8000 tdw.

Deadweight-ul cuprinde :

marf i balast ;

combustibil, ulei, ap tehnic i ap potabil n tancuri;

rezerve, echipaj, bagaje;

2.5 VITEZA

Viteza navei pe chil dreapt, cu corpul proaspt vopsit i carena curat, n ap adnc, la o intensitate a vntului nu mai mare de 30 pe scara Beaufort i starea mrii maxim 20, la pescajul de plin ncrcare, i 85% din puterea maxim continu a motorului principal va fi de cel puin 14 Nd.

Aceast vitez se va deduce din rezultatele probelor de mar cu nava n balast.

2.6 MOTOR PRINCIPAL

Propulsia navei este asigurat de un motor principal avnd urmtoarele caracteristici:

Producator:

MITSUBISHI

Tipul motorului:

UEC45LAP1

Putere:

3530 kW

Turaie:

158 RPM

Masa motorului:

111 t.

2.7 AUTONOMIE

Rezervele de combustibil, ulei, ap, hran, asigur navei o autonomie de 5.000 Mm la o vitez de exploatare de 14 Nd la 85% din puterea maxim continu a motorului principal i un consum specific de 170g/kW(h.

2.8 STRUCTURA ECHIPAJULUI

Echipajul navei este compus din 23 persoane dup cum urmeaz: cpitan de curs lung, ef mecanic, ef electrician, cpitan secund, 2 ofieri de cart punte, 2 ofieri de cart maini, ofier ef staie RTG, ofier RTG, 1 ofieri electricieni, ef mecanic secund, ajutor ofier mecanic, ef echipaj, ef timonier, 2 timonieri, 2 marinari, 2 motoriti, un buctar, un sanitar: TOTAL: 23 persoane.

2.9 STABILITATE I ASIET

Stabilitatea navei va satisface criteriile de stabilitate ale Germanischer Lloyd ediia 2004.La navigaia n balast, pescajul pupa asigur funcionare normal a elicei, iar pescajul prova este mai mare de 2,5% din lungimea navei.2.10 COMPARTIMENTAREA NAVEI

Nava are o construcie metalic, realizat din table i profile, mbinate prin sudur.

Nava este mprit n urmtoarele compartimente, delimitate de 5 perei transversali etani:

- pic pupa

- compartimentul de maini

- magazii de mrfuri nr.1: 3

- pic prova.

Dublul fund este extins ntre pereii picurilor. Structura dublului fund a fost calculat n acord cu destinaia magaziilor i pentru utilizarea graifrelor la descrcarea mrfii. 2.11 MATERIALE

Corpul rezistent al navei proiectate: tablele nveliului, osatura format din platband, profile cu bulb, platbenzi confecionate din table va fi executat din oel cu o limit de curgere cu ReH = 235N / mm2 .

Toate elementele ce compun structura corpului navei se execut din oel laminat sub form de table i sub form de profile.

Ca profile se folosesc: profile simple cu bulb i profile compuse cum ar fi profilul T format din inim i platband.

2.12 INSTALAIILE NAVEI

Nava proiectat este dotat cu instalaii de bord care asigur securitatea de navigaie, integritatea mrfii transportate, condiiile necesare pentru locuit i pentru desfurarea activitii echipajului.

Instalaiile navale existente pe nav sunt: instalaii cu tubulaturi; instalaii mecanice de punte; instalaii mecanice de bord, instalaii electrice; instalaii de navigaie,

radiocomunicaii, comunicri i semnalizri.

Instalaiile cu tubulaturi sunt utilizate pentru:

ambarcarea i asigurarea cu combustibil, ulei i ap potabil i tehnic,

evacuarea apelor uzate i de santin,

balastarea navei,

acionarea hidraulic a mecanismelor de bord,

sistemul de control i msurare a pescajului navei,

sistemul de control al ncrcrii magaziilor,

stingerea incendiilor de la bordul navei cu CO2,

sistemul de aer condiionat i ventilaie n magazii, spaii sociale i cabine,

nclzirea spaiilor sociale i cabinelor,

sistemul de pstrare (refrigerare) al proviziilor,

sistemului de preparare al apei de but,

incinerarea resturilor menajere.

Instalaiile mecanice de punte deservesc diferite echipamente de punte sunt:

instalaia de ancorare i manevr,

instalaia de lumini,

instalaia de crm,

instalaia de salvare,

instalaia de ncrcare a proviziilor,

instalaia de acces la bordul navei (scri de bord i pilot).Instalaiile aferente compartimentului de maini

instalaii de rcire a M.P. i D.G -urilor cu ap de mare i ap dulce,

instalaii de ungere a M.P. i D.G -urilor,

instalaia de transfer i alimentare cu combustibil a M.P. i D.G-urilor,

instalaia de aer comprimat,

instalaia de abur,

instalaia de evacuare gaze arse de la instalaia de la M.P. i D.G.,

instalaia de ventilaie a compartimentului maini,

Instalaii de navigaie, radiocomunicaii, comunicri i semnalizri

n conformitate cu cerinele societii de clasificare precum i cu ultimele tendine n domeniu nava este dotat cu urmtoarele echipamente de navigaie :

- sistem integrat de comunicri interioare,

- receptor de navigaie prin satelit,

- calculator de ncrcare,

- radare,

- sonda ultrason.CAPITOLUL 3

DETERMINAREA DIMENSIUNILOR PRINCIPALE SI A COEFICIENTILOR DE FINETE3.1 CALCULUL DEPLASAMENTULUI NAVEI CUNOASCND DEADWEIGHT-UL

Legtura dintre deplasamentul navei ( si deadweight Dw a fost stabilit pe baze statistice sub forma:

Unde:(Dw- coeficent de utilizare al deplasamentului

Valorile informative sunt date n tabelul de mai jos:

Tipul navei(Dw(u

Vrachiere0,67 0,790,60 0,69

Vom alege

[ t ]

O estimare brut a raportului ( Dw/( ), pentru nave de constructie si amenajri normale este oferit de Sch(nemann.

* Se va intra n diagrama dup Sch(nemann (fig. 4.1 pag. 57Proiectarea Navei) cu viteza navei v=14 Nd si deadweight-ul, si se va scoate raportul Dw/(= 0,72.

De aici rezult:

[ t ]

Vom adopta un deplasament al navei:

3.2 LUNGIMEA NAVEI

Suprafaa udat a navei este influenat de lungimea navei. n acelai timp, mrimea suprafeei udate influeneaz rezistena de frecare, cea mai nsemnat component a rezistenei la naintare pentru navele cu vitez mic. Proiectantul va trebui s in cont de limitarea lungimii navei. Pentru meninerea deadweight-ului, vor rezulta forme mai pline la extremiti, fapt ce va genera o cretere a rezistenei de form.

Micorarea rezistenei de val, la aceeai vitez, se realizeaz prin mrirea lungimii navei.

Rezult c lungimea navei este un parametru foarte important, cu implicaii majore asupra rezistenei la naintare a navei i implicit asupra puterii instalaiei de propulsie, precum i asupra volumului necesar ncrcturii utile.

n mod uzual, se utilizeaz n calcule lungimea ntre perpendicularele planului de forme Lpp i lungimea la plutirea de plin ncrcare LWL, ntre care exist relaia:

De asemenea, se definete i lungimea relativ, l, cu relaia:

Dup Galin lungimea ntre perpendiculare poate fi determinat cu relaia:

Unde:

- v este viteza de serviciu [Nd]

- coeficientul c are valorea c = 7,17 pentru nave cu o elice i v = 11 16,5 Nd - deplasamentul volumetric

Jager propune pentru lungimea ntre perpendiculare urmtoarea relaie de calcul:

Unde:

- v este viteza de serviciu a navei [Nd] - coeficientul b are valorea b = 5/6 pentru nave obinuite (vrachiere, petroliere)

O relaie de calcul foate simpl aparine lui Noghid:

Unele expresii sunt utilizate pentru determinarea lungimii relative.

Astfel, cu relaia lui Pozdiunin:

Literatura de specialitate recomand i utilizarea urmtoarelor relaie pentru nave de transportat mrfuri uscate:

De asemenea pentru navele care circul prin Canalul Panama (limea este limitat la 32,3 m):

Vom adopta lungimea navei :

Calculare numrului Froude:

3.3 LIMEA NAVEI

ntr-o prim aproximaie, calculul limii navei se poate realiza cu ajutorul unor relaii statistice.

Dup Arkenbout i Schokker, limea navei B, msurat n metri, nu trebuie s fie mai mic dect valoarea calculat cu formula:

De asemenea, Watson recomand urmtoarea relaie pentru nave de transport mrfuri uscate:

Sanderson propune urmatoarea relaie:

Van Manen indic urmtoarea relaie de calcul ale raportului L/B pentru nave de transport mrfuri uscate:

Vom adopta limea navei :

3.4 PESCAJUL NAVEIPescajul navei se determin n funcie de raportul B/T, astfel:Valorile uzuale ale raportului B/T propuse de Galin pentru vrachiere i petroliere sunt:

Van Manen recomand utilizarea urmtoarei relaii pentru calculul raportului B/T n cazul navelor de transport mrfuri uscate:

Vom adopta pescajul navei :

3.5 INLIMEA DE CONSTRUCIEConform conveniei LoadLines 66, navele sunt mprite n dou tipuri:Tipul A nave proiectate pentru a transporta numai ncrcturi lichide n vrac, deschiderile n tancurile de marf fiind de mici dimensiuni, nchise cu capace rezistente i prevzute cu garnituri etane.

Tipul B orice nav ce nu satsiface condiiile pentru tipul A

Astfel n funcie de aceasta mprire rezult o valoare a bordului liber de baz n funcie de lungimea navei si pentru nava de proiectat avem un bord liber de baz:

Acest bord va fi corectat n funcie de particularitile navei, astfel:

La navele cu , bordul liber de baz trebuie s fie multiplicat prin factorul

Dac raportul , bordul liber de baz va fi majorat cu valoarea

Rezult astfel un bord liber corectat:

Pentru vrachiere i petroliere raportul L/D se poate calcula n funcie de deadweight (Dw), cu expresia:

Vom adopta nlimea de construcie navei :

3.6 COEFICIENI DE FINEE

3.6.1 Coeficientul bloc

n general, exist o dependen liniar ntre coeficientul de finee bloc CB i numrul Froude, exprimat sub forma:

Unde a i b sunt constante.

Aik propune urmtoarea expresie general pentru :

Pentru petroliere i vrachiere sunt recomandate urmtoarele expresii:

Ayre recomand pentru nave de transportat mrfuri uscate cu :

Coeficientul bloc se determin cu relaia general:

Unde:

- este volumul real al carenei navei - L este lungimea navei - B este limea navei - T este pescajul considerat

Adoptm coeficientul bloc:

3.6.2 Coeficientul suprafeei plutirii

n stadiul preliminar de proiectare se pot folosi unele relaii empirice care furnizeaz valorile coeficientului de finee al suprafeei plutirii Cw, n funcie de coeficientul bloc.Coeficientul suprafeei plutirii se determin cu expresia:

Unde:

AWL este aria suprafeei plutirii de plin ncrcare

Pentru navele cu forme clasice se recomand:

formula lui Galin:

formula lui Lyndbladom:

formula de calcul:

pentru navele cu bulb:

pentru navele de transport, formula lui Bronikov:

Adoptm un coeficient al plutirii:

Din relaia putem determina

3.6.3 Coeficientul seciunii maestre

Coeficientul de finee al seciunii maestre, CM, se calculeaz n funcie de aria seciunii maestre, AM, cu expresia:

Literatura de specialitate recomand urmtoarele relaii generale:

pe baze statistice:

formula lui Noghid pentru :

dup Jeleazkov:

Adoptm un coeficient al seciunii maestre:

Din relaia putem determina

3.6.4 Coeficientul prismatic longitudinal

Coeficientul de finee prismatic longitudinal are o mare influen asupra rezistenei la naintare i se determin cu relaia general:

n funcie de valorile numrului Froude, Fn, literatura de specialitate furnizeaz urmtoarele expresii pentru calculul coeficientului prismatic longitudinal:pentru pe baza unor prelucrri statistice:

pentru dup Aik:

pentru dup Noghid:

Adoptm un coeficient prismatic longitudinal:

CAPITOLUL 4FORMELE NAVEI

4.1 Generarea planului de forme utiliznd programul MultiSurf Pentru generarea suprafeelor navei s-au construit urmatoarele curbe :

curba ce delimiteaz poriunea cilindric a navei

cubele punilor

curba fundului navei

curbele de profil pupa respectiv prova

Cu ajutorul acestor curbe s-au generat suprafeele definitorii ale navei pe care s-au generat contururile corespunzatoare plutirilor,longitudinalelor si cuplelor navei.

n urma construciei contururilor navei s-au extras cu ajutorul programului Multisurf tabelul cu semilaimile navei si caracteristicile contururilor navei :

Dimensiuni principale:

DimensiuneaSimbolValoarea [m]

LungimeLpp119

LimeB16,8

nlime de construcieD9,52

Pescaj de calculd6,8

Distana ntre cuple ntregiL5,95

Distana ntre plutiri ntregid0,68

4.2 TABELUL DE TRASAJ PE CUPLE

Tabelul cu abscisele cuplelor

CuplaX

[m]

- 1/2-60.988

0-59.5

1/4-58.013

1/2-56.525

3/4-55.038

1-53.55

1 1/4-52.063

1 1/2-50.575

1 3/4-49.088

2-47.6

3-41.65

4-35.7

5-29.75

6-23.8

7-17.85

8-11.9

9-5.95

100

115.95

1211.9

1317.85

1423.8

1529.75

1635.7

1741.65

1847.6

18 1/449.0875

18 1/250.575

18 3/452.0625

1953.55

19 1/455.0375

19 1/256.525

19 3/458.0125

2059.5

20 1/460.9875

20 1/262.475

Tabelul cu cotele plutirilor

WLz

[m]

00.00

10.68

21.36

32.04

42.72

53.40

64.08

74.76

85.44

96.12

106.80

117.48

128.16

138.84

149.52

Tabelul cu ordonatele longitudinalelor

Longitudinalay

[m]

0 (PD)0

I2.10

II4.20

III6.30

IV (Bord plat)8.40

Semilimile naveiC\WL01234567891011121314

--------1.2333.6464.6455.245.6325.8796.052

0--------1.9354.1135.015.5445.916.1536.323

1/4--------2.6834.5935.3715.846.1676.46.563

1/2--------3.4975.0555.7126.126.4096.6236.777

3/4---0.245----4.2755.4726.0236.3776.6336.8266.969

1-0.4140.6960.8550.8620.619-1.4234.9275.8386.3036.6126.8387.0117.143

1 1/4-0.7831.0411.2141.2891.3191.5593.0015.4486.166.5566.8267.0267.1817.301

1 1/20.2931.0721.3581.5611.6941.882.4354.1945.8776.4466.7847.027.1977.3357.443

1 3/40.5621.3711.6981.9352.1292.4593.2965.0966.2386.7026.997.1977.3537.4757.572

20.821.7092.0832.3572.6213.1054.1965.7476.556.937.1777.3577.4947.6027.688

32.1693.5814.1344.5585.176.0186.7177.1927.4617.6377.7647.8617.9377.9988.048

43.6495.756.3846.9017.3067.5817.7827.9258.0238.0948.1488.198.2248.2518.273

54.6527.3487.8978.088.1588.2158.268.2938.3178.3358.3488.3598.3678.3748.379

65.0037.9088.3358.388.3868.3918.3948.3968.3978.3988.3998.3998.48.48.4

75.0467.9558.3668.48.48.48.48.48.48.48.48.48.48.48.4

85.0467.9558.3668.48.48.48.48.48.48.48.48.48.48.48.4

95.0467.9558.3668.48.48.48.48.48.48.48.48.48.48.48.4

105.0467.9558.3668.48.48.48.48.48.48.48.48.48.48.48.4

C\WL01234567891011121314

115.0467.9558.3668.48.48.48.48.48.48.48.48.48.48.48.4

125.0467.9558.3668.48.48.48.48.48.48.48.48.48.48.48.4

135.0467.9558.3668.48.48.48.48.48.48.48.48.48.48.48.4

144.9997.9248.3428.3838.3888.3928.3958.3978.3988.3998.3998.48.48.48.4

154.5397.5248.0048.1038.1578.2038.2418.2738.2998.3218.3388.3528.3638.3728.379

162.7046.0786.7476.9987.1927.3667.5197.6537.7697.8717.9588.0338.0978.1528.198

171.2864.0374.7985.1525.4315.7175.9986.2676.5196.7516.9637.1567.337.4867.625

180.6822.6153.1963.523.6923.8774.1334.4434.7755.1095.4365.756.0446.3186.573

18 1/40.5612.3832.9143.2163.3773.4963.6893.9714.34.6474.9955.3335.6535.9556.238

18 1/20.4352.1782.6642.9483.1053.1733.2843.5113.8214.1714.5354.8955.2385.5645.872

18 3/40.3081.9882.4372.7042.8542.9022.9313.0663.3363.6814.0584.4364.7975.1445.476

19-1.8042.2222.4742.6172.6692.6432.6472.8393.1663.5563.9514.3284.6915.043

19 1/4-1.6132.012.2492.3862.4452.3992.2812.332.6113.0163.4263.8184.1984.569

19 1/2-1.4031.7882.0192.1522.2122.1752.0071.8161.9812.4072.8353.2463.6464.037

19 3/4-1.1441.5411.7691.8991.961.941.7761.3411.1771.6512.1222.573.0033.423

20-0.7521.2311.4721.6061.6671.6571.5130.98-0.131.0991.6822.1952.674

20 1/4--0.7361.061.2191.2881.2821.1460.608----0.9191.638

20 1/2----0.4570.6070.60.315-------

Tabel de nlimi pe longitudinale

Long0IIIIIIIV

Cupla(PD)(bord plat)

- 1/25.3515.5956.44511.039

05.2625.4696.179.413

1/45.1745.3445.9028.516

1/25.0715.2175.6497.88

3/41.7285.0715.4177.31

10.3674.8715.1996.794

1 1/40.0204.47856.327

1 1/203.7734.7615.9

1 3/402.6344.4595.509

201.3964.0825.147

3001.4613.648

4000.0361.252

50000.184

60000.087.051

70000.0741.623

80000.0741.623

90000.0741.623

100000.0741.623

110000.0741.623

120000.0741.623

130000.0741.623

140000.0796.27

150000.157

16000.0890.84

1700.0520.7874.846

1800.3194.2358.794

18 1/400.4395.2399.676

18 1/200.5996.17410.531

18 3/400.827.05211.371

1901.1257.92712.204

19 1/40.0201.5788.84313.041

19 1/20.0832.4039.80713.892

19 3/40.2077.44710.822

200.4348.7111.89

20 1/40.91310.05613.012

20 1/22.28111.46214.184

Extremitile plutirilor

WLzPupaProva

XppYXpvY

00.00-51.520.0053.460.00

10.68-54.140.0059.510.00

21.36-54.790.0061.670.00

32.04-55.150.0062.320.00

42.72-54.940.0062.680.00

53.40-53.390.0062.830.00

64.08-54.140.0062.830.00

74.76-62.240.0062.580.00

85.44-62.370.4661.620.00

96.12-62.493.2558.970.00

106.80-62.614.2959.510.00

117.48-62.734.9160.120.00

128.16-62.7315.2660.420.00

138.84-62.8535.4860.730.00

149.52-62.9755.6261.34

Linia punii i a parapetului

CuplaPuntea in bord Puntea in P.D.SageataParapetDunetaTeuga

XYZXYZFXYZXYZXYZ

Extr. pp-63.135.74610.36063.8830.00010.6990.339-63.7395.89013.780-63.5235.88412.57250.5007.17012.932

- 1/2-60.98756.19710.298-60.98750.00010.6250.327-60.9886.47713.695-60.9886.41112.494---

0 -59.506.42510.26-59.50000.00010.5880.328-59.5006.71913.644-59.5006.65112.444---

1/4-58.016.64510.233-58.01250.00010.5510.318-58.0136.95613.604-58.0136.87912.402---

1/2-56.536.86410.206-56.52500.00010.5130.307-56.5257.17813.572-56.5257.10212.372---

3/4-55.047.05610.171-55.03750.00010.4380.267-55.0387.33613.526-55.0387.26812.333---

1 -53.557.20310.124-53.55000.00010.4050.281-53.5507.48713.484-53.5507.41512.290---

1 1/4-52.067.34910.077-52.06250.00010.4060.329-52.0637.63513.454-52.0637.56312.253---

1 1/2-50.587.48210.032-50.57500.00010.4000.368-50.5757.74513.419-50.5757.68912.223---

1 3/4-49.097.5949.992-49.08750.00010.3640.372-49.0887.83913.381-49.0887.78412.181---

2 -47.607.7069.951-47.60000.00010.3280.377-47.6007.93313.345-47.6007.87812.143---

3 -41.658.0539.814-41.65000.00010.2920.478-41.6508.19313.211-41.6508.15912.012---

4 -35.708.2639.699-35.70000.00010.1590.460-35.7008.32412.224------

5 -29.758.3749.605-29.75000.00010.0420.437-29.7508.38210.806------

6 -23.808.3989.546-23.80000.0009.9490.403-23.8008.39910.745------

7 -17.858.4009.523-17.85000.0009.8980.375-17.8508.40010.723------

8 -11.908.4009.52-11.90000.0009.8870.367-11.9008.40010.720------

9 -5.958.4009.52-5.95000.0009.8870.367-5.9508.40010.720------

10 0.008.4009.520.00000.0009.8870.3670.0008.40010.720------

CuplaPuntea in bord Puntea in P.D.SageataParapetDunetaTeuga

XYZXYZFXYZXYZXYZ

11 5.958.4009.525.95000.0009.8870.3675.9508.40010.720------

12 11.908.4009.5211.90000.0009.8870.36711.9008.40010.723------

13 17.858.4009.54717.85000.0009.8870.34017.8508.40010.747------

14 23.808.3989.63423.80000.0009.8770.24323.8008.40010.833------

15 29.758.3739.79229.75000.00010.0260.23429.7508.38610.992------

16 35.708.20710.01435.70000.00010.1390.12535.7008.27111.215------

17 41.657.74310.28141.65000.00010.243-0.03841.6507.92611.480------

18 47.606.91210.58447.60000.00010.6240.04047.6007.41812.358------

18 1/449.096.64210.66349.08750.00010.9280.26549.0887.45813.267------

18 1/250.586.35510.74250.57500.00010.9880.24650.5757.51414.180---50.5757.15712.937

18 3/452.066.02210.81952.06250.00011.0640.24552.0637.29014.219---52.0636.90213.018

19 53.555.68110.89753.55000.00011.2140.31753.5507.08314.303---53.5506.65513.102

19 1/455.045.26710.9855.03750.00011.2880.30855.0386.83214.387---55.0386.32013.183

19 1/256.534.84511.06256.52500.00011.3600.29856.5256.50914.472---56.5255.99113.272

19 3/458.014.30511.14758.01250.00011.4290.28258.0136.18114.562---58.0135.55313.348

20 59.503.71811.23359.50000.00011.4930.26059.5005.71814.647---59.5005.06413.439

20 1/460.992.96911.32860.98750.00011.5470.21960.9885.21814.740---60.9884.49113.536

20 1/262.4751.90411.42362.47500.00011.5800.15762.4754.56914.831---62.4753.74513.626

Extr. Pv63.736011.50863.73600.00011.5080.00066.9770.00015.120-37.2508.29111.92165.8320.00013.844

CAPITOLUL 5CALCULE HIDROSTATICE PE PLUTIRI DREPTE

5.1 CALCULUL HIDROSTATIC PE PLUTIRI

Relaii de baz

Aria plutirii

Abscisa centrului de plutire

Momentul de inerie n raport cu axa x

Momentul de inerie n raport cu axa y

Momentul de inerie n raport cu axa yF

Metoda numeric de integrare: metoda trapezelor

unde:

f

funcia de integrat, respectiv f=y, f=xy, f=y3 sau f=x2y, dup caz.

i = 0 .. nindicele punctelor de calcul

xi,

abscisele n punctele de calcul

fi,

valoarea funciei la abscisele n punctele de calcul

n tabele se calculeaz sumele care reprezint:

Aw=2S1

MYW = 2S2

XF = MYW /Aw

Ix = 2/3 S3

Iy = 2S4

IyF = Iy - (XF)2Aw

WL=0.00z=0.000

Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)

Extr. pp-51.52-0.000-0.000-0.00-0.00-

- 1/4----------

0----------

1/4----------

1/2----------

3/4----------

1----------

1 1/4----------

1 1/2-50.580.9440.2930.138-14.818-6.990.030.01749.44353.59

1 3/4-49.091.4880.5620.636-27.587-31.540.180.151354.191564.57

2-47.601.4880.8201.028-39.032-49.550.550.541857.922389.01

3-41.655.9502.1698.892-90.339-384.8810.2032.003762.6116721.10

4-35.705.9503.64917.309-130.269-656.3148.59174.904650.6125029.35

5-29.755.9504.65224.695-138.397-799.28100.67444.054117.3126084.58

6-23.805.9505.00328.724-119.071-765.97125.23672.052833.9020679.85

7-17.855.9505.04629.896-90.071-622.20128.48754.781607.7713213.96

8-11.905.9505.04630.024-60.047-446.60128.48764.47714.566908.94

9-5.955.9505.04630.024-30.024-267.96128.48764.47178.642657.29

100.005.9505.04630.0240.000-89.32128.48764.470.00531.46

115.955.9505.04630.02430.02489.32128.48764.47178.64531.46

1211.905.9505.04630.02460.047267.96128.48764.47714.562657.29

1317.855.9505.04630.02490.071446.60128.48764.471607.776908.94

1423.805.9504.99929.884118.976621.92124.93753.892831.6313207.22

1529.755.9504.53928.376135.035755.6893.51649.864017.3020375.57

1635.705.9502.70421.54896.533688.9119.77337.023446.2222203.97

1741.655.9501.28611.87053.562446.532.1365.142230.8516889.30

1847.605.9500.6825.85532.463255.920.327.271545.2511233.90

18 1/449.091.4880.5610.92427.53844.630.180.371351.782154.66

18 1/250.581.4880.4350.74122.00036.840.080.191112.661832.92

18 3/452.061.4880.3080.55316.03528.290.030.08834.841448.45

19----------

19 1/4----------

19 1/2----------

19 3/4----------

20----------

20 1/4----------

20 1/2----------

Extr. Pv53.460.0000.0000.0000.0000.000.000.000.000.00

Sume391.210-437.998479.12215577.37

WL=1z=0.68


Extr. pp-54.140-0.000-0.000-0.000-0.000-

- 1/4----------

0----------

1/4----------

1/2----------

3/4----------

1-53.5500.5900.4140.122-22.170-6.5390.0710.0211187.187350.161

1 1/4-52.0632.0770.7830.813-40.765-42.3430.4800.4992122.3252204.459

1 1/2-50.5753.5651.0721.911-54.216-96.6381.2322.1962741.9944887.468

1 3/4-49.0881.4881.3711.817-67.299-90.3772.5772.8333303.5384496.365

2-47.6001.4881.7092.291-81.348-110.5564.9915.6293872.1845336.943

3-41.6505.9503.58115.738-149.149-685.72945.921151.4656212.04130000.570

4-35.7005.9505.75027.760-205.275-1054.410190.109702.1917328.31840282.567

5-29.7505.9507.34838.967-218.603-1261.037396.7411745.8816503.43941149.476

6-23.8005.9507.90845.387-188.210-1210.270494.5382651.5574479.40832673.969

7-17.8505.9507.95547.192-141.997-982.366503.4092968.8922534.64220866.797

8-11.9005.9507.95547.332-94.665-704.067503.4092995.2811126.50810891.920

9-5.9505.9507.95547.332-47.332-422.440503.4092995.281281.6274189.200

100.0005.9507.95547.3320.000-140.813503.4092995.2810.000837.840

115.9505.9507.95547.33247.332140.813503.4092995.281281.627837.840

1211.9005.9507.95547.33294.665422.440503.4092995.2811126.5084189.200

1317.8505.9507.95547.332141.997704.067503.4092995.2812534.64210891.920

1423.8005.9507.92447.240188.591983.499497.5462977.8404488.47120893.760

1529.7505.9507.52445.958223.8391226.980425.9382747.3656659.21033164.350

1635.7005.9506.07840.466216.9851311.450224.5341935.1547746.35042856.542

1741.6505.9504.03730.092168.1411145.74965.792863.7217003.07543879.539

1847.6005.9502.61519.790124.474870.53017.882248.9315924.96238460.910

18 1/449.0881.4882.3833.717116.976179.57813.53223.3645742.0358677.330

18 1/250.5751.4882.1783.392110.152168.92610.33217.7495570.9558414.037

18 3/452.0631.4881.9883.098103.500158.9047.85713.5285388.4828151.081

1953.5501.4881.8042.82096.604148.8285.87110.2105173.1557855.217

19 1/455.0381.4881.6132.54188.775137.8764.1977.4884885.9817481.482

19 1/256.5251.4881.4032.24379.305125.0102.7625.1754482.6916967.950

19 3/458.0131.4881.1441.89466.366108.3431.4973.1683850.0756197.495

2059.5001.4880.7521.41044.74482.6380.4251.4302662.2684843.555

20 1/4----------

20 1/2----------

Extr. Pv59.5130.0130.0000.0050.0000.2910.0000.0030.00017.290

Sume670.6581108.33635057.973451947.234

WL=2z=1.36


Extr. pp-54.785-0.000-0.000-0.000-0.000-

- 1/4----------

0----------

1/4----------

1/2----------

3/4----------

1-53.5501.2350.6960.430-37.271-23.0220.3370.2081995.8511232.837

1 1/4-52.0631.4881.0411.292-54.197-68.0291.1281.0902821.6353583.005

1 1/2-50.5751.4881.3581.784-68.681-91.3902.5042.7023473.5344682.032

1 3/4-49.0881.4881.6982.273-83.351-113.0734.8965.5044091.4715626.473

2-47.6001.4882.0832.812-99.151-135.7359.03810.3634719.5786553.218

3-41.6505.9504.13418.496-172.181-807.21270.650237.0717171.34335375.490

4-35.7005.9506.38431.291-227.909-1190.267260.183984.2278136.34445540.369

5-29.7505.9507.89742.486-234.936-1376.963492.4782239.1656989.33944998.906

6-23.8005.9508.33548.290-198.373-1289.094579.0513187.7974721.27734839.082

7-17.8505.9508.36649.685-149.333-1034.426585.5363464.6462665.59621975.948

8-11.9005.9508.36649.778-99.555-740.443585.5363483.9391184.70911454.658

9-5.9505.9508.36649.778-49.778-444.266585.5363483.939296.1774405.638

100.0005.9508.36649.7780.000-148.089585.5363483.9390.000881.128

115.9505.9508.36649.77849.778148.089585.5363483.939296.177881.128

1211.9005.9508.36649.77899.555444.266585.5363483.9391184.7094405.638

1317.8505.9508.36649.778149.333740.443585.5363483.9392665.59611454.658

1423.8005.9508.34249.706198.5401034.921580.5113468.9904725.24221987.744

1529.7505.9508.00448.629238.1191299.059512.7683252.5077084.04035132.616

1635.7005.9506.74743.884240.8681424.986307.1372439.2198598.98446656.997

1741.6505.9504.79834.346199.8371311.096110.4541242.3338323.19950343.493

1847.6005.9503.19623.782152.1301047.10032.645425.7207241.36946304.588

18 1/449.0881.4882.9144.544143.041219.53324.74442.6837021.52410608.027

18 1/250.5751.4882.6644.149134.732206.59418.90632.4656814.06110290.216

18 3/452.0631.4882.4373.794126.876194.57114.47324.8266605.4989980.797

1953.5501.4882.2223.465118.988182.86210.97118.9246371.8139651.875

19 1/455.0381.4882.0103.148110.625170.7758.12114.1996088.5449267.390

19 1/256.5251.4881.7882.825101.067157.4465.71610.2915712.7958777.246

19 3/458.0131.4881.5412.47689.397141.6583.6596.9735186.1598106.097

2059.5001.4881.2312.06273.245120.9651.8654.1094358.0487098.504

20 1/460.9881.4880.7361.46344.88787.8600.3991.6842737.5345277.339

20 1/2----------

Extr. Pv61.6680.6800.0000.2500.00015.2700.0000.1360.000931.309

Sume726.0291485.48442021.465518304.443

WL=3.00z=2.04


Extr. pp-55.154-0.000-0.000-0.000-0.000-

- 1/4----------

0----------

1/4----------

1/2----------

3/4-55.0380.1160.2450.014-13.484-0.7820.0150.001742.13643.044

1-53.5501.4880.8550.818-45.785-44.0820.6250.4762451.8002375.490

1 1/4-52.0631.4881.2141.539-63.204-81.0611.7891.7963290.5524270.874

1 1/2-50.5751.4881.5612.064-78.948-105.7253.8044.1603992.7745416.973

1 3/4-49.0881.4881.9352.600-94.984-129.3627.2458.2184662.5426437.391

2-47.6001.4882.3573.192-112.193-154.08813.09415.1275340.3967439.686

3-41.6505.9504.55820.572-189.841-898.55194.694320.6707906.86539410.603

4-35.7005.9506.90134.091-246.366-1297.714328.6521259.4548795.25549688.809

5-29.7505.9508.08044.568-240.380-1448.068527.5142547.0947151.30547441.017

6-23.8005.9508.38048.969-199.444-1308.476588.4803320.0844746.76735396.765

7-17.8505.9508.40049.921-149.940-1039.417592.7043514.0242676.42922084.009

8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210

9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542

100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708

115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708

1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542

1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210

1423.8005.9508.38349.929199.5151039.630589.1133515.9054748.46722089.064

1529.7505.9508.10349.046241.0641310.724532.0323335.4057171.66135462.381

1635.7005.9506.99844.925249.8291460.406342.7062602.3458918.88147869.364

1741.6505.9505.15236.146214.5811381.618136.7501426.3828937.29053122.110

1847.6005.9503.52025.799167.5521136.84543.614536.5847975.47550315.477

18 1/449.0881.4883.2165.010157.865242.02933.26257.1777749.21811695.240

18 1/250.5751.4882.9484.584149.095228.30225.62043.7947540.48511371.716

18 3/452.0631.4882.7044.204140.777215.59219.77133.7597329.20311059.330

1953.5501.4882.4743.851132.483203.23715.14325.9677094.44910727.591

19 1/455.0381.4882.2493.513123.779190.59511.37519.7236812.50510343.297

19 1/256.5251.4882.0193.174114.124176.9418.23014.5826450.8589864.626

19 3/458.0131.4881.7692.817102.624161.2065.53610.2385953.4819225.727

2059.5001.4881.4722.41087.584141.4673.1906.4895211.2488303.767

20 1/460.9881.4881.0601.88364.647113.2221.1913.2583942.6446808.207

20 1/2----------

Extr. Pv62.3201.3330.0000.7060.00043.0770.0000.7940.0002627.181

Sume746.2271537.56543783.036554508.661

WL=4.00z=2.72


Extr. pp-54.938-0.000-0.000-0.000-0.000-

- 1/4----------

0----------

1/4----------

1/2----------

3/4----------

1-53.5501.3880.8620.598-46.160-32.0400.6410.4452471.8731715.727

1 1/4-52.0631.4881.2891.600-67.109-84.2442.1422.0693493.8404436.999

1 1/2-50.5751.4881.6942.219-85.674-113.6324.8615.2084332.9655821.186

1 3/4-49.0881.4882.1292.843-104.507-141.4479.65010.7935130.0017038.081

2-47.6001.4882.6213.533-124.760-170.51718.00520.5695938.5578232.240

3-41.6505.9505.17023.178-215.331-1011.768138.188464.6768968.51544348.540

4-35.7005.9507.30637.116-260.824-1416.560389.9771571.2929311.42454382.819

5-29.7505.9508.15846.005-242.701-1497.986542.9392775.4257220.34049181.997

6-23.8005.9508.38649.218-199.587-1315.805589.7453369.7364750.16635612.255

7-17.8505.9508.40049.938-149.940-1039.842592.7043517.7872676.42922094.120

8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210

9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542

100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708

115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708

1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542

1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210

1423.8005.9508.38849.944199.6341039.984590.1673519.0434751.29922097.490

1529.7505.9508.15749.221242.6711315.858542.7393370.3987219.45535612.992

1635.7005.9507.19245.663256.7541485.790372.0052721.3659166.13248747.121

1741.6505.9505.43137.553226.2011436.793160.1911583.2859421.27855297.545

1847.6005.9503.69227.141175.7391195.77350.325626.2878365.18652914.730

18 1/449.0881.4883.3775.258165.768253.99638.51266.0728137.16112273.620

18 1/250.5751.4883.1054.821157.035240.08529.93550.9087942.06411958.923

18 3/452.0631.4882.8544.432148.586227.30623.24739.5547735.77811660.395

1953.5501.4882.6174.069140.140214.74117.92330.6207504.51611334.969

19 1/455.0381.4882.3863.721131.319201.89813.58323.4337227.49610956.933

19 1/256.5251.4882.1523.375121.642188.1409.96617.5156875.80310489.328

19 3/458.0131.4881.8993.013110.166172.4076.84812.5066390.9909867.177

2059.5001.4881.6062.60795.557153.0064.1428.1745685.6428981.995

20 1/460.9881.4881.2192.10174.344126.3641.8114.4284534.0407600.888

20 1/262.4751.4880.4571.24728.55176.5280.0951.4181783.7284698.840

Extr. Pv62.6790.2040.0000.0460.0002.9050.0000.0100.000181.494

Sume760.3421507.73244972.550581157.328

WL=5.00z=3.40


Extr. pp-53.394-0.000-0.000-0.000-0.000-

- 1/4----------

0----------

1/4----------

1/2----------

3/4----------

1-53.550-0.1560.619-0.048-33.1472.5850.237-0.0181775.046-138.453

1 1/4-52.0631.4881.3191.441-68.670-75.7272.2951.8833575.1553979.212

1 1/2-50.5751.4881.8802.379-95.081-121.7906.6456.6494808.7226235.508

1 3/4-49.0881.4882.4593.227-120.706-160.49214.86916.0015925.1647983.327

2-47.6001.4883.1054.138-147.798-199.70029.93533.3237035.1859639.259

3-41.6505.9506.01827.141-250.650-1185.382217.950737.45910439.56051987.366

4-35.7005.9507.58140.457-270.642-1550.842435.6921944.5849661.90959801.869

5-29.7505.9508.21546.993-244.396-1532.238554.3992945.5217270.78850374.774

6-23.8005.9508.39149.403-199.706-1321.204590.8013406.9714752.99835770.765

7-17.8505.9508.40049.953-149.940-1040.196592.7043520.9272676.42922102.545

8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210

9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542

100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708

115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708

1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542

1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210

1423.8005.9508.39249.956199.7301040.267591.0123521.5564753.56422104.231

1529.7505.9508.20349.370244.0391320.212551.9733400.3827260.16835740.853

1635.7005.9507.36646.318262.9661508.341399.6642831.1229387.89349527.982

1741.6505.9505.71738.922238.1131490.711186.8551744.8949917.40957433.273

1847.6005.9503.87728.542184.5451257.40858.276729.2648784.35255637.736

18 1/449.0881.4883.4965.484171.610264.89042.72875.1228423.90112798.638

18 1/250.5751.4883.1734.960160.474246.98831.94655.5398115.99712301.549

18 3/452.0631.4882.9024.518151.085231.72324.43941.9367865.88211886.522

1953.5501.4882.6694.143142.925218.67019.01332.3187653.63111542.638

19 1/455.0381.4882.4453.804134.567206.38414.61625.0127406.21411200.760

19 1/256.5251.4882.2123.464125.033193.07710.82318.9217067.50710764.830

19 3/458.0131.4881.9603.103113.705177.5617.53013.6506596.28210162.444

2059.5001.4881.6672.69899.187158.3384.6329.0455901.5979295.298

20 1/460.9881.4881.2882.19878.552132.1932.1375.0354790.6847952.384

20 1/262.4751.4880.6071.40937.92286.6280.2241.7562369.1975325.162

Extr. Pv62.8330.3580.0000.1090.0006.7800.0000.0400.000423.576

Sume773.9621355.18746278.421605452.969

WL=6z=4.08


Extr. pp-54.140-0.000-0.000-0.000-0.000-

- 1/4----------

0----------

1/4----------

1/2----------

3/4----------

1----------

1 1/4-52.0632.0771.5591.619-81.165-84.3073.7893.9364225.6764389.209

1 1/2-50.5751.4882.4352.971-123.150-151.96014.43813.5566228.3187775.157

1 3/4-49.0881.4883.2964.262-161.792-211.92635.80637.3697941.98410539.162

2-47.6001.4884.1965.572-199.730-268.88273.87781.5779507.12912977.778

3-41.6505.9506.71732.466-279.763-1426.491303.0581121.38111652.13162948.798

4-35.7005.9507.78243.135-277.817-1658.802471.2742303.6399918.08164171.381

5-29.7505.9508.26047.725-245.735-1557.568563.5603078.6327310.61651255.375

6-23.8005.9508.39449.546-199.777-1325.399591.4353436.1104754.69735894.308

7-17.8505.9508.40049.962-149.940-1040.409592.7043522.8132676.42922107.601

8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210

9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542

100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708

115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708

1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542

1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210

1423.8005.9508.39549.965199.8011040.479591.6463523.4424755.26422109.286

1529.7505.9508.24149.492245.1701323.788559.6803425.1957293.80035845.965

1635.7005.9507.51946.886268.4281527.954425.0892929.6899582.89050208.154

1741.6505.9505.99840.213249.8171541.779215.7841906.59910404.86659463.574

1847.6005.9504.13330.140196.7311328.47970.599851.9899364.38658813.524

18 1/449.0881.4883.6895.818181.084281.00050.20389.8468888.95013575.919

18 1/250.5751.4883.2845.186166.088258.20935.41763.6798399.91612858.594

18 3/452.0631.4882.9314.622152.595237.02125.18045.0697944.48712156.150

1953.5501.4882.6434.146141.533218.75818.46332.4597579.07311545.648

19 1/455.0381.4882.3993.750132.035203.46613.80724.0007266.87411041.674

19 1/256.5251.4882.1753.402122.942189.63910.28917.9216949.28910573.272

19 3/458.0131.4881.9403.061112.544175.1437.30113.0836528.97310024.458

2059.5001.4881.6572.67598.592157.0324.5508.8145866.1949218.906

20 1/460.9881.4881.2822.18678.186131.4782.1074.9514768.3677909.455

20 1/262.4751.4880.6001.40037.48586.0300.2161.7282341.8755288.243

Extr. Pv62.8270.3520.0000.1050.0006.5880.0000.0380.000411.597

Sume790.185981.10147697.045636722.109

WL=7.00z=4.76


Extr. pp-62.243-0.000-0.000-0.000-0.000-

- 1/4----------

0----------

1/4----------

1/2----------

3/4----------

1-53.5508.6931.4236.185-76.202-331.2042.88112.5244080.59817735.978

1 1/4-52.0631.4883.0013.290-156.240-172.87827.02722.2448134.2229084.773

1 1/2-50.5751.4884.1945.351-212.112-273.96173.77174.96810727.54214028.437

1 3/4-49.0881.4885.0966.909-250.150-343.807132.339153.29412279.23317111.289

2-47.6001.4885.7478.064-273.557-389.507189.812239.60013021.32318817.288

3-41.6505.9507.19238.494-299.547-1704.984372.0051671.40612476.12475854.905

4-35.7005.9507.92544.973-282.923-1732.846497.7352587.47610100.33367164.961

5-29.7505.9508.29348.249-246.717-1575.677570.3423177.5267339.82351884.466

6-23.8005.9508.39649.650-199.825-1328.461591.8583457.5434755.83035984.569

7-17.8505.9508.40049.968-149.940-1040.550592.7043524.0712676.42922110.971

8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210

9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542

100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708

115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708

1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542

1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210

1423.8005.9508.39749.971199.8491040.621592.0693524.7004756.39722112.656

1529.7505.9508.27349.593246.1221326.762566.2253445.9257322.12235933.593

1635.7005.9507.65347.380273.2121545.018448.2243017.9869753.67250800.487

1741.6505.9506.26741.412261.0211589.342246.1382065.72810871.50661359.904

1847.6005.9504.44331.862211.4871405.70987.706993.18610066.77262291.376

18 1/449.0881.4883.9716.258194.926302.27062.618111.8039568.45314603.698

18 1/250.5751.4883.5115.565177.569277.04343.28178.7628980.54313795.816

18 3/452.0631.4883.0664.892159.624250.78728.82153.6268310.40512860.143

1953.5501.4882.6474.249141.747224.14418.54635.2307590.54411826.331

19 1/455.0381.4882.2813.665125.541198.79511.86822.6216909.43710784.361

19 1/256.5251.4882.0073.189113.446177.7468.08414.8396412.5179908.203

19 3/458.0131.4881.7762.814103.030161.0045.60210.1795977.0399214.732

2059.5001.4881.5132.44690.024143.5843.4646.7425356.3988429.244

20 1/460.9881.4881.1461.97869.892118.9371.5053.6954262.5197154.069

20 1/262.4751.4880.3151.08719.68066.6190.0311.1431229.4854084.677

Extr. Pv62.5780.1030.0000.0160.0001.0160.0000.0020.00063.462

Sume817.390-64.47949466.354698619.312

WL=8.00z=5.44


Extr. pp-62.365-0.458--28.532-0.096-1779.397-

- 1/4-60.9881.3781.2331.164-75.198-71.4441.8751.3574586.1134384.245

0-59.5001.4881.9352.356-115.133-141.5587.2456.7836850.3848505.894

1/4-58.0131.4882.6833.435-155.648-201.39319.31419.7539029.50311810.666

1/2-56.5251.4883.4974.596-197.668-262.77842.76546.17111173.17915025.745

3/4-55.0381.4884.2755.780-235.285-322.00978.12889.91412949.51517941.254

1-53.5501.4884.9276.844-263.841-371.225119.605147.06414128.67820139.406

1 1/4-52.0631.4885.4487.716-283.637-407.186161.700209.22114766.82521491.030

1 1/2-50.5751.4885.8778.423-297.229-432.019202.986271.23615032.37122163.152

1 3/4-49.0881.4886.2389.011-306.208-448.806242.737331.50715030.97722359.614

2-47.6001.4886.5509.511-311.780-459.628281.011389.53814840.72822217.080

3-41.6505.9507.46141.683-310.751-1852.029415.3282071.60912942.76582655.890

4-35.7005.9508.02346.065-286.421-1776.586516.4292771.97610225.23368924.794

5-29.7505.9508.31748.612-247.431-1588.209575.3083247.9157361.06552319.237

6-23.8005.9508.39749.724-199.849-1330.656592.0693472.9464756.39736049.448

7-17.8505.9508.40049.971-149.940-1040.621592.7043524.7002676.42922112.656

8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210

9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542

100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708

115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708

1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542

1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210

1423.8005.9508.39849.974199.8721040.692592.2813525.3304756.96322114.342

1529.7505.9508.29949.674246.8951329.134571.5803462.4877345.13436003.738

1635.7005.9507.76947.802277.3531559.639468.9163095.4789901.51351308.773

1741.6505.9506.51942.507271.5161632.887277.0402219.22111308.65663100.252

1847.6005.9504.77533.600227.2901483.949108.8731148.09210819.00465829.788

18 1/449.0881.4884.3006.750211.076326.03579.507140.10810361.20515752.781

18 1/250.5751.4883.8216.040193.247300.71555.787100.6259773.47114975.165

18 3/452.0631.4883.3365.323173.681272.90237.12669.1049042.24113994.186

1953.5501.4882.8394.593152.028242.24622.88244.6318141.12312780.127

19 1/455.0381.4882.3303.844128.237208.44812.64926.4277057.86511304.247

19 1/256.5251.4881.8163.084102.649171.7225.98913.8625802.2579564.716

19 3/458.0131.4881.3412.34877.795134.2052.4116.2484513.0697672.024

2059.5001.4880.9801.72658.310101.2280.9412.4943469.4455936.995

20 1/460.9881.4880.6081.18137.08070.9470.2250.8672261.4414262.346

20 1/2----------

Extr. Pv61.6220.6350.0000.1930.00011.7710.0000.0710.000717.894

Sume853.409-1819.62751616.265797036.409

WL=9.00z=6.12


Extr. pp-62.487-3.251--203.158-34.366-12694.757-

- 1/4-60.9881.5003.6465.171-222.360-319.03348.46762.10513561.20619685.409

0-59.5001.4884.1135.771-244.724-347.39469.57987.79714561.04820915.927

1/4-58.0131.4884.5936.475-266.451-380.18696.892123.81315457.51322326.305

1/2-56.5251.4885.0557.176-285.734-410.688129.171168.13416151.10723508.911

3/4-55.0381.4885.4727.829-301.165-436.506163.847217.93216575.38024340.325

1-53.5501.4885.8388.412-312.625-456.506198.972269.84716741.06324779.105

1 1/4-52.0631.4886.1608.924-320.705-471.039233.745321.83316696.70424869.340

1 1/2-50.5751.4886.4469.376-326.006-480.992267.837373.05216487.77624680.957

1 3/4-49.0881.4886.7029.779-328.984-487.149301.032423.09716149.02324273.619

2-47.6001.4886.93010.139-329.868-490.021332.813471.42215701.71723688.988

3-41.6505.9507.63743.337-318.081-1927.648445.4192315.23813248.07686125.633

4-35.7005.9508.09446.800-288.956-1805.935530.2612902.64710315.72270102.298

5-29.7505.9508.33548.876-247.966-1597.343579.0513300.2037376.99652635.836

6-23.8005.9508.39849.781-199.872-1332.320592.2813484.7124756.96336098.528

7-17.8505.9508.40049.974-149.940-1040.692592.7043525.3302676.42922114.342

8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210

9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542

100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708

115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708

1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542

1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210

1423.8005.9508.39949.977199.8961040.763592.4923525.9594757.53022116.027

1529.7505.9508.32149.742247.5501331.152576.1383476.6757364.60536063.351

1635.7005.9507.87148.171280.9951572.420487.6293164.70810031.51151753.445

1741.6505.9506.75143.500281.1791672.467307.6842366.05611711.11264684.302

1847.6005.9505.10935.284243.1881559.993133.3551312.08811575.76869278.466

18 1/449.0881.4884.6477.256228.110350.528100.350173.81811197.33116937.492

18 1/250.5751.4884.1716.558210.948326.54972.564128.60510668.71216262.869

18 3/452.0631.4883.6815.840191.642299.42749.87791.0659977.36515355.519

1953.5501.4883.1665.092169.539268.62931.73560.6989078.83014173.045

19 1/455.0381.4882.6114.297143.703232.97417.80036.8417909.04912634.735

19 1/256.5251.4881.9813.415111.976190.1617.77419.0216329.44510589.880

19 3/458.0131.4881.1772.34968.281134.0661.6316.9953961.1357653.619

20----------

20 1/4----------

20 1/2----------

Extr. Pv58.9750.9620.0000.5660.00032.8460.0000.7840.0001905.504

Sume879.746-2971.47853570.006873172.695

WL=10.00z=6.80


Extr. pp-62.609-4.291--268.680-79.030-16821.763-

- 1/4-60.9881.6224.6457.245-283.287-447.507100.221145.32817276.96227645.542

0-59.5001.4885.0107.181-298.095-432.403125.752168.06717736.65326041.376

1/4-58.0131.4885.3717.721-311.585-453.450154.941208.76518075.83326635.536

1/2-56.5251.4885.7128.243-322.871-471.877186.365253.84618250.27227017.540

3/4-55.0381.4886.0238.728-331.491-486.681218.494301.11418244.42827142.933

1-53.5501.4886.3039.167-337.526-497.581250.404348.74318074.49927012.202

1 1/4-52.0631.4886.5569.564-341.322-504.893281.784395.81517770.06426659.393

1 1/2-50.5751.4886.7849.922-343.101-509.039312.218441.78917352.32326122.275

1 3/4-49.0881.4886.99010.244-343.122-510.378341.532486.22616842.98325432.759

2-47.6001.4887.17710.537-341.625-509.280369.682528.96616261.36024621.355

3-41.6505.9507.76444.449-323.371-1978.363468.0122492.14013468.38588445.991

4-35.7005.9508.14847.338-290.884-1827.406540.9453001.64610384.54570962.467

5-29.7505.9508.34849.076-248.353-1604.229581.7653340.0617388.50252874.813

6-23.8005.9508.39949.822-199.896-1333.541592.4923493.4154757.53036134.443

7-17.8505.9508.40049.977-149.940-1040.763592.7043525.9592676.42922116.027

8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210

9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542

100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708

115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708

1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542

1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210

1423.8005.9508.39949.977199.8961040.763592.4923525.9594757.53022116.027

1529.7505.9508.33849.793248.0561332.656579.6763487.2027379.65136108.113

1635.7005.9507.95848.481284.1011583.164503.9783223.87310142.39152128.077

1741.6505.9506.96344.390290.0091707.976337.5902503.66512078.87366108.261

1847.6005.9505.43636.887258.7541632.569160.6341482.21612316.67172576.744

18 1/449.0881.4884.9957.758245.192374.810124.625212.16212035.86518112.199

18 1/250.5751.4884.5357.088229.358352.94693.268162.05811599.76217578.998

18 3/452.0631.4884.0586.391211.270327.71766.825119.06910999.22516807.996

1953.5501.4883.5565.663190.424298.75944.96683.14410197.19415764.837

19 1/455.0381.4883.0164.888165.993265.08527.43453.8489135.84514378.948

19 1/256.5251.4882.4074.033136.056224.64913.94530.7767690.54712514.629

19 3/458.0131.4881.6513.01895.779172.4274.50013.7195556.3589852.386

2059.5001.4880.1301.3257.73576.9880.0023.349460.2334474.839

20 1/4----------

20 1/2----------

Extr. Pv59.5130.0130.0000.0010.0000.0500.0000.0000.0002.989

Sume898.787-3216.83255192.451927008.616

WL=11.00z=7.48


Extr. pp-62.731-4.912--308.141-118.523-19330.021-

- 1/4-60.9881.7445.2408.850-319.575-547.211143.878228.74819490.05033841.396

0-59.5001.4885.5448.021-329.868-483.023170.400233.74419627.14629093.414

1/4-58.0131.4885.8408.467-338.793-497.317199.177274.87319654.22929215.523

1/2-56.5251.4886.1208.895-345.933-509.265229.221318.62119553.86329161.018

3/4-55.0381.4886.3779.295-350.974-518.325259.328363.35819316.73928910.010

1-53.5501.4886.6129.661-354.073-524.379289.067407.86918960.58828468.762

1 1/4-52.0631.4886.8269.995-355.379-527.654318.053451.54518501.90027862.725

1 1/2-50.5751.4887.02010.298-355.037-528.371345.948493.85117955.97127115.541

1 3/4-49.0881.4887.19710.574-353.283-526.812372.782534.55517341.76626252.692

2-47.6001.4887.35710.825-350.193-523.210398.201573.41816669.19625295.654

3-41.6505.9507.86145.274-327.411-2015.871485.7732629.82213636.65490159.903

4-35.7005.9508.19047.752-292.383-1843.886549.3533079.50110438.07371622.312

5-29.7505.9508.35949.233-248.680-1609.663584.0673371.9267398.23753063.024

6-23.8005.9508.39949.855-199.896-1334.515592.4923500.2654757.53036163.407

7-17.8505.9508.40049.977-149.940-1040.763592.7043525.9592676.42922116.027

8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210

9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542

100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708

115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708

1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542

1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210

1423.8005.9508.40049.980199.9201040.834592.7043526.5894758.09622117.712

1529.7505.9508.35249.837248.4721333.966582.6013496.5337392.04236146.661

1635.7005.9508.03348.745286.7781592.369518.3623275.36610237.97852449.310

1741.6505.9507.15645.187298.0471739.856366.4472632.30712413.67467388.666

1847.6005.9505.75038.395273.7001700.949190.1091655.75513028.12075689.338

18 1/449.0881.4885.3338.243261.784398.266151.675254.20212850.30419247.078

18 1/250.5751.4884.8957.607247.565378.828117.289200.04212520.58118869.596

18 3/452.0631.4884.4366.940230.949355.89587.292152.15712023.79518254.880

1953.5501.4883.9516.238211.576329.12861.677110.79511329.89717369.309

19 1/455.0381.4883.4265.487188.558297.60040.21375.78010377.78716145.090

19 1/256.5251.4882.8354.657160.248259.42522.78646.8559058.03914455.396

19 3/458.0131.4882.1223.687123.103210.7429.55524.0537141.48512048.396

2059.5001.4881.0992.39665.391140.1921.3278.0943890.7358205.214

20 1/4----------

20 1/2----------

Extr. Pv60.1230.6230.0000.3420.00020.3710.0000.4140.0001212.054

Sume914.591-3231.84656606.532971559.029

WL=12.00z=8.16


Extr. pp-62.731-5.264--330.218-145.867-20714.936-

- 1/4-60.9881.7445.6329.499-343.482-587.298178.644282.89220948.08436319.738

0-59.5001.4885.9108.584-351.645-517.000206.425286.39520922.87831141.528

1/4-58.0131.4886.1678.982-357.763-527.622234.543327.97020754.73130997.721

1/2-56.5251.4886.4099.353-362.269-535.524263.251370.23420477.24030666.278

3/4-55.0381.4886.6339.700-365.064-540.954291.830412.84220092.19530173.517

1-53.5501.4886.83810.019-366.175-543.859319.733454.85019608.66629527.516

1 1/4-52.0631.4887.02610.311-365.791-544.400346.836495.76119044.00028747.921

1 1/2-50.5751.4887.19710.578-363.988-542.773372.782535.21618408.70727855.451

1 3/4-49.0881.4887.35310.822-360.940-539.166397.552572.93517717.66126868.986

2-47.6001.4887.49411.042-356.714-533.756420.863608.69616979.60525806.092

3-41.6505.9507.93745.907-330.576-2044.689499.9992739.56513768.49291475.591

4-35.7005.9508.22448.079-293.597-1856.914556.2233142.26210481.40672143.447

5-29.7505.9508.36749.358-248.918-1613.982585.7463397.3597405.31853213.003

6-23.8005.9508.40049.882-199.920-1335.294592.7043505.8894758.09636186.156

7-17.8505.9508.40049.980-149.940-1040.834592.7043526.5892676.42922117.712

8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210

9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542

100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708

115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708

1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542

1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210

1423.8005.9508.40049.980199.9201040.834592.7043526.5894758.09622117.712

1529.7505.9508.36349.870248.7991334.940584.9063503.3917401.77836175.624

1635.7005.9508.09748.969289.0631600.140530.8513319.37710319.54652720.937

1741.6505.9507.33045.895305.2951768.213393.8332750.93412715.51668529.308

1847.6005.9506.04439.788287.6941764.142220.7871828.49413694.25378569.064

18 1/449.0881.4885.6538.700277.492420.357180.650298.56813621.37120315.995

18 1/250.5751.4885.2388.100264.912403.413143.713241.24513397.91720095.595

18 3/452.0631.4884.7977.464249.744382.775110.385188.98513002.28719635.152

1953.5501.4884.3286.787231.764358.12281.070142.39512410.98418901.120

19 1/455.0381.4883.8186.059210.133328.66155.655101.69011565.20517832.290

19 1/256.5251.4883.2465.254183.480292.75034.20266.83110371.21516315.212

19 3/458.0131.4882.5704.326149.092247.35116.97538.0628649.20714146.439

2059.5001.4881.6823.162100.079185.3214.75916.1645954.70110861.656

20 1/4----------

20 1/2----------

Extr. Pv60.4200.9200.0000.7730.00046.0150.0002.1880.0002737.903

Sume927.103-3131.03157843.9001005813.589

WL=13.00z=8.84


Extr. pp-62.853-5.479--344.377-164.485-21645.143-

- 1/4-60.9881.8665.87910.594-358.546-655.651203.194342.95221866.79440585.760

0-59.5001.4886.1538.949-366.104-538.958232.949324.38121783.15832464.652

1/4-58.0131.4886.4009.336-371.280-548.429262.144368.22521538.88132220.767

1/2-56.5251.4886.6239.686-374.365-554.574290.512411.03821160.98631758.026

3/4-55.0381.4886.82610.003-375.686-557.850318.053452.62020676.81731116.866

1-53.5501.4887.01110.291-375.439-558.649344.620492.86220104.76130331.299

1 1/4-52.0631.4887.18110.555-373.861-557.292370.301531.72219464.12929429.362

1 1/2-50.5751.4887.33510.796-370.968-553.966394.639568.92418761.68828430.451

1 3/4-49.0881.4887.47511.015-366.929-548.811417.670604.15518011.63027350.155

2-47.6001.4887.60211.214-361.855-542.033439.323637.38917224.30826206.729

3-41.6505.9507.99846.410-333.117-2067.541511.6162829.04313874.31192518.389

4-35.7005.9508.25148.341-294.561-1867.340561.7203193.17410515.81772560.629

5-29.7505.9508.37449.459-249.127-1617.469587.2173418.0887411.51353333.808

6-23.8005.9508.40049.903-199.920-1335.913592.7043510.2664758.09636204.588

7-17.8505.9508.40049.980-149.940-1040.834592.7043526.5892676.42922117.712

8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210

9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542

100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708

115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708

1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542

1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210

1423.8005.9508.40049.980199.9201040.834592.7043526.5894758.09622117.712

1529.7505.9508.37249.897249.0671335.736586.7973509.0157409.74336199.322

1635.7005.9508.15249.159291.0261606.778541.7423357.40310389.64252953.173

1741.6505.9507.48646.523311.7921793.384419.5172859.74512986.13369542.931

1847.6005.9506.31841.067300.7371822.273252.1961998.34714315.07281221.083

18 1/449.0881.4885.9559.128292.316441.083211.176344.63314349.06521318.951

18 1/250.5751.4885.5648.567281.399426.701172.251285.17414231.77021256.996

18 3/452.0631.4885.1447.964267.810408.474136.114229.34613942.83220954.860

1953.5501.4884.6917.315251.203386.016103.228178.01013451.92320374.849

19 1/455.0381.4884.1986.611231.047358.67473.982131.80012716.27319462.596

19 1/256.5251.4883.6465.834206.090325.12148.46791.07211649.24618121.854

19 3/458.0131.4883.0034.945174.212282.84927.08156.18910106.44716180.796

2059.5001.4882.1953.866130.603226.70510.57628.0077770.84913296.239

20 1/460.9881.4880.9192.31656.048138.8210.7768.4433418.1988321.853

20 1/2----------

Extr. Pv60.733-0.2550.000-0.1170.000-7.1330.000-0.0990.000-435.005

Sume939.467-2958.99458974.6371041136.322

WL=14.00z=9.52


Extr. pp-62.975-5.624--354.195-177.919-22305.436-

- 1/4-60.9881.9886.05211.603-369.096-718.771221.665397.08722510.26444535.602

0-59.5001.4886.3239.204-376.219-554.328252.796352.88022385.00133390.853

1/4-58.0131.4886.5639.584-380.736-562.985282.688398.26622087.44933076.385

1/2-56.5251.4886.7779.922-383.070-568.081311.252441.74321653.02832531.980

3/4-55.0381.4886.96910.224-383.556-570.178338.463483.22621109.98231804.988

1-53.5501.4887.14310.496-382.508-569.760364.453522.79420483.28530934.992

1 1/4-52.0631.4887.30110.743-380.108-567.196389.177560.51219789.38929952.801

1 1/2-50.5751.4887.44310.966-376.430-562.675412.329596.12019037.93328877.821

1 3/4-49.0881.4887.57211.167-371.691-556.414434.142629.56318245.36027729.449

2-47.6001.4887.68811.350-365.949-548.619454.402660.85517419.16326525.489

3-41.6505.9508.04846.815-335.199-2085.915521.2712902.62813961.04793356.123

4-35.7005.9508.27348.555-295.346-1875.872566.2253235.30210543.85672902.085

5-29.7505.9508.37949.540-249.275-1620.249588.2703434.6227415.93953430.389

6-23.8005.9508.40049.918-199.920-1336.356592.7043513.3974758.09636217.753

7-17.8505.9508.40049.980-149.940-1040.834592.7043526.5892676.42922117.712

8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210

9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542

100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708

115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708

1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542

1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210

1423.8005.9508.40049.980199.9201040.834592.7043526.5894758.09622117.712

1529.7505.9508.37949.918249.2751336.356588.2703513.3977415.93936217.753

1635.7005.9508.19849.317292.6691612.283550.9653389.22310448.26953146.018

1741.6505.9507.62547.073317.5811815.493443.3222958.00413227.25970434.696

1847.6005.9506.57342.239312.8751875.607283.9822163.73014892.84083657.296

18 1/449.0881.4886.2389.528306.208460.443242.737391.74715030.97722255.839

18 1/250.5751.4885.8729.007296.976448.618202.469331.12215019.58122350.103

18 3/452.0631.4885.4768.440285.094432.915164.206272.71514842.71922210.086

1953.5501.4885.0437.824270.053412.891128.253217.51714461.31921794.879

19 1/455.0381.4884.5697.149251.466387.88095.381166.32813840.07921049.165

19 1/256.5251.4884.0376.401228.191356.74565.792119.87312898.52019886.833

19 3/458.0131.4883.4235.548198.577317.40940.10778.76311519.93618161.227

2059.5001.4882.6744.535159.103266.02419.12044.0509466.62915608.757

20 1/460.9881.4881.6383.20799.898192.6324.39517.4896092.50011572.102

20 1/2----------

Extr. Pv61.3430.3560.0000.2910.00017.7570.0000.7810.0001082.957

Sume950.401-2764.34760006.4431072548.765

Centralizatorul de carene drepte

Coeficient de nveli i apendici(1+k)=1,006

Densitate ap1,025 t/m3WLzAWxFVxBzBIxIyFrR

00782.42-1.120.000.00-1.120.005652.75430174.02--

10.681341.321.65722.07744.560.630.4323371.98900231.1832.371246.74

21.361452.062.051671.821723.901.330.7728014.311030530.1716.76616.41

32.041492.452.062672.952756.211.601.1229188.691102681.1610.92412.53

42.721520.681.983697.423812.591.721.4729981.701156335.108.11312.74

53.41547.921.754740.754888.421.751.8230852.281206160.146.51254.42

64.081580.371.245804.375985.171.702.1731798.031271007.935.48218.97

74.761634.78-0.086897.527112.371.522.5332977.571397228.454.78202.57

85.441706.82-2.138033.668283.911.152.9034410.841586313.254.28197.46

96.121759.49-3.389212.219499.170.653.2635713.341726272.143.88187.39

106.81797.57-3.5810421.6110746.240.173.6436794.971830990.623.53175.69

117.481829.18-3.5311654.7012017.75-0.234.0137737.691920277.613.24164.76

128.161854.21-3.3812907.0613309.11-0.544.3838562.601990478.812.99154.22

138.841878.93-3.1514176.3214617.92-0.784.7539316.422063633.042.77145.57

149.521900.80-2.9115461.4315943.06-0.975.1240004.302129016.712.59137.70

unde:

Deplasamentul n ap srat

= (1+k)V

Abscisa centrului de volum

xB = MyOz / V

Cota centrului de volum

zB = MxOy / V

Raza metacentric transversal r=Ix/V

Raza metacentric longitudinal R = IyF/V5.2 CARACTERISTICI DE VOLUM

Relaii de baz

Volumul

Momentul static n raport cu planul yOz

Momentul static n raport cu planul xOy

Metoda numeric de integrare: metoda trapezelor.

unde:

f

funcia de integrat, respectiv f=Aw, f=xFAw sau f= zAw dup caz.

i = 1 .. nindicele plutirilor pn la care se face calculul

j = 0 .. iindicele plutirilor de calcul

zj,

cotele plutirilor de calcul

fj,

valoarea funciei la cotele de calcul

Centralizatorul calculului de volum

WLzdzAWs(AW)VxFs(xFAW)MyOzs(zAW)MxOy

00-782.42-0.00-1.12-0.00-0.00

10.70.681341.321061.87722.071.65670.35455.84456.05310.11

21.40.681452.061396.691671.822.052593.822219.641443.451291.66

320.681492.451472.262672.952.063023.054275.312509.702998.25

42.70.681520.681506.573697.421.983045.306346.113590.435439.75

53.40.681547.921534.304740.751.752862.928292.904699.608635.48

64.10.681580.371564.155804.371.242336.299881.575855.4212617.17

74.80.681634.781607.576897.52-0.08916.6210504.877114.7317455.18

85.40.681706.821670.808033.66-2.13-1884.119223.688533.3223257.84

96.10.681759.491733.169212.21-3.38-4791.115965.7310026.5930075.93

106.80.681797.571778.5310421.61-3.58-6188.311757.6811495.8037893.07

117.50.681829.181813.3811654.70-3.53-6448.68-2627.4212952.8946701.03

128.20.681854.211841.6912907.06-3.38-6362.88-6954.1814406.3056497.31

138.80.681878.931866.5714176.32-3.15-6090.03-11095.3915870.0567288.95

149.50.681900.801889.8715461.43-2.91-5723.34-14987.2717352.7079088.79

unde:

dzi = zi - zi-1

sumele pariale si(f) = 1/2(fi+fi-1)

Vi = Vi-1+si(Aw)dzi

(MyOz)i = (MyOz)i-1 + si(xFAw)dzi

(MxOy)i = (MxOy)i-1 + si(zAw)dzi5.3 COEFICIENTI DE FINEE

WLzAWVCWCBCPV

00782.420.000.39--

10.71341.32722.070.670.530.792

21.41452.061671.820.730.610.847

321492.452672.950.750.660.878

42.71520.683697.420.760.680.894

53.41547.924740.750.770.700.901

64.11580.375804.370.790.710.900

74.81634.786897.520.820.720.886

85.41706.828033.660.850.740.865

96.11759.499212.210.880.750.856

106.81797.5710421.610.8990.7670.853

117.51829.1811654.700.910.780.852

128.21854.2112907.060.930.790.853

138.81878.9314176.320.940.800.853

149.51900.8015461.430.950.810.854

unde:

CW = Aw/LB

CB = V/LBz

CPV = CB/CW

5.4 TRASAREA DIAGRAMEI DE CARENE DREPTEStabilirea formatului de hrtie i a scrilor de reprezentare

Se va face conform urmtoarelor considerente:

- claritatea curbelor;

- evitarea aglomerrii curbelor;

- scrile s fie rotunde.

Am ales formatul A3 landscape pentru reprezentarea diagramelor de carene drepte.

Exprimarea scrilor se poate face n dou moduri:

- prin axe multiple fiecare ax la scara ei

- prin explicitare:

z,zB1cm

0.5 m

Aw1cm

100 m2xF,xB1cm

5 m

V,

1cm

500 m3Ix1cm

1500 m4IyF1cm

50000 m4r1cm

1 m

R1cm

30 m

Am ales a doua variant.

Pe diagram se traseaz explicit linia de plutire i cuplul maestru corespunztor graficelor pentru XB i XF.Trasarea propriu-zis a curbelor de carene drepte

Se face conform urmtoarelor observaii:

- curbele trec prin punctele de definiie

- curbele sunt aviate

- curbele se inscripioneaz.

Pentru trasarea diagramelor de carene drepte am utilizat programul AUTOCAD. Aa cum am artat la capitolul 5.2, pentru calculul de carene drepte am utilizat, programul EXCEL. Tabelul final coninnd valorile pe plutiri ale variabilelor ce formeaz diagrama de carene l-am completat cu scrile de reprezentare. Apoi am obinut reprezentarea grafica a curbelor de carene drepte.

CAPITOLUL 6

DETERMINAREA DEPLASAMENTULUI NAVEI GOALE, DEADWEIGHT-ULUI SI A REZERVELOR6.1 Clasificarea grupelor de mase

n conformitate cu ecuaia flotabilitii, deplasamentul navei () reprezint masa volumului de fluid dezlocuit de carena navei:

Cu s-a notat densitatea apei, iar este deplasamentul volumetric (volumul real al carenei, incluznd volumul nveliului tablelor i al apendicilor).

Deplasamentul navei se calculeaz prin nsumarea urmtoarelor grupe principale de mase:

S-au utilizat notaiile:

- masa corpului navei;

- masa instalaiei de propulsie;

- masa amenajrilor i instalaiilor de corp i punte, cu mecanismele i echipamentele aferente;

- masa combustibilului, uleiului i apei aferente instalaiei de propulsie;

- masa ncrcturii utile;

- masa echipajului i a bagajelor;

- masa rezervelor echipajului;

- masa balastului lichid;

- rezerva de deplasament.

Un parametru caracteristic pentru navele de transportat mrfuri este deadweight-ul (Dw) care cuprinde urmtoarele grupe de mase:

Celelalte grupe de mase care nu intr n componena deadweight-ului alctuiesc deplasamentul navei goale ().

6.2 Determinarea grupelor de mase prin metoda Parsons

Coeficientul bloc calculat la 80% din nlimea de construcie:

- coeficientul bloc al navei

Masa corpului navei

Numrul Lloyd

Unde: B laimea navei

T pescajul navei

D nlimea de construcie

Coeficientul conform TABEL 11. VII

Masa motorului

- puterea motorului in kW

- turaia motorului

Masa amenajrilor i instalaiilor de corp i punte cu mecanismele i echipamentele aferente:

Deplasamentul navei goale complet dotat, cu rezervDenumirea componenteiValoare [t]

Mc masa corpului metallic1920,93

Mm masa instalaiei de propulsie367,04

Mai - masa amenajrilor i instalaiilor de corp i punte368,928

g0 nava goala complet dotat net2656,9

RD rezerva de deplasament106,28

g nava goala complet dotat cu rezerv2763,18

Componentele deadweight-ului masa util, masa combustibilului, uleiului i apei aferente instalaiei de propulsie

Masa util

Masa combustibilului, uleiului i a apei aferente instalaiei de propulsie

Unde - coeficient de siguran

- consumul specific de combustibil

- autonomie

- puterea motorului in kW

- viteza de serviciu a navei

Unde - masa apei, - masa uleiului

Masa echipajului i a bagajelor

Masa rezervelor echipajului

Masa de balast lichid

CAPITOLUL 7

CALCULUL REZISTENTEI LA INAINTARE SI A PROPULSIEI

7.1 .CALCULUL REZISTENEI LA NAINTARE

n faza iniial de proiectare a unei nave, determinarea rezistenei la naintare ocup un loc important prin necesitatea unei estimri ct mai exacte a acesteia, tiut fiind faptul c rezistena la naintare condiioneaz puterea instalaiei de propulsie, caracteristicile propulsorului i ale liniei de arbori, i prin acestea, estimarea corect a maselor de la bordul navei i asigurarea performanelor nautice.

Pentru determinarea rezistenei la naintare a unei nave exist mai multe ci, plecnd de la determinri pe nave n mrime natural pn la formule aproximative menite s ofere doar o idee asupra ordinului de mrime.

Metoda se bazeaz pe diagramele obinute n cadrul testelor experimentale pe serii de modele, care prezint variaia coeficientului rezistenei rezidue pentru nave cu forme standard (form normal a seciunilor, pup moderat de crucitor, raport B/T = 2,5 i poziie normal a centrului de caren).

Conform acestei metode, rezistena total la naintare a navei se determin cu relaia :

- unde CT este coeficientul rezistenei totale la naintare a navei, care se calculeaz nsumnd coeficientul rezistenei de frecare a plcii plane echivalente CF0, coeficientul de corelare de la model la nav CA, coeficientul total al rezistenei rezidue , coeficientul rezistenei aerului CAA i coeficientul coreciei de rezisten la manevrabilitate CAS :

Coeficientul rezistenei de frecare se calculeaz cu formula ITTC-1957

Coeficientul de corelare model-nav ine cont de rugozitatea carenei reale i include i efectul de scar n trecerea de la model la nav. Se recomand alegerea coeficientului CA n funcie de lungimea navei, n conformitate cu datele prezentate n tabelul de mai jos. Pentru valori intermediare ale lungimii, mrimea CA se va stabili prin interpolare.Lungimea naveiCA

501500,000350,0004

1502100,0002

2102600,0001

2603000

300350-0,0001

350400-0,00025

Coeficientul rezistenei rezidue, CR, se determin din diagramele specifice metodei Harvald, n funcie de valorile numrului Froude, coeficientului prismatic longitudinal CP i raportului LWL/(1/3. Numrul Froude i coeficientul prismatic se calculeaz n funcie de lungimea la plutire, LWL.

Coeficientul total al rezistenei rezidue include urmtoarele corecii :

Corecia este datorat raportului B/T diferit de cel standard i se determin cu expresia :

Corecia ine cont de poziia longitudinal a centrului de caren, LCB.

Poziia standard este definit n diagrame, prin intermediul unei funcii liniare de numrul Froude. Abscisa centrului de caren este exprimat n procente din lungimea la plutire. Dac abscisa se afl n prova seciunii maestre, ea este considerat pozitiv.

Dac centrul de caren al navei proiectate se afl n prova centrului de caren standard, atunci corecia coeficientului rezistenei rezidue se determin cu relaia :

n care (LCB este diferena dintre abscisa centrului de caren al navei proiectate i valoarea standard a abscisei centrului de caren, calculate n procente din lungimea la plutire.

n continuare prezint mersul de calcul al metodei Guldhammer Harvald cu ajutorul cruia am calculat rezistena la naintare pentru nava tip vrachier 8000 tdw.

Pentru efectuarea calcului respectiv este necesara cunoasterea vitezei de mars a navei pe care trebuie s-o asigure elicea. De aceea calculele trebuie efectuate tabelar pentru mai multe viteze, trei sau cinci, gama ce va contine si viteza de serviciu a navei preconizata.

v1213141516Nd

v6.1736.6887.202227.7178.231m/s

Fr0.180.190.210.220.24

Re6.324E+086.851E+087.378E+089.238E+089.854E+08

103*Cf01.621510751.605060771.590051.545779701.53341428

103*CA0.3240.3240.3240.3240.324

CM =0.9830.9830.9830.9830.983

CB =0.750.750.750.750.75

CP =0.7620.7620.7620.7620.762

103*CR0.790.821.051.211.7l =

103*C1-0.005-0.005-0.005-0.005-0.005

LCB1.50.80.1-0.5-1.1

Abaterea dLCB0.020.080.180.250.32

103*C20.030.0640.018-0.125-0.352

103*C3-0.080.3947-0.1057-0.1477-0.1753

103*C40.03160.03280.0420.04840.068

103*CRT0.7671.3071.0000.9811.236

103*CF1.945510751.929060771.914051.869779701.85741428

103*CAA0.070.070.070.070.07

103*CAS0.040.040.040.040.04

103*CT2.822404863.345854893.023652.960773823.20340840

CBpp0.73260.73260.73260.73260.7326

Sudata2946.9162946.9162946.9162946.9162946.916

RT162.4502255226.012428236.87850266.2724687327.786294kN

RF194.940271.215284.254319.527393.344kN

PE1203.4311813.8252047.2622465.6833237.654kW

PD1784.6812689.8913036.0763656.5924801.420kW

Numrul Froude pentru viteza de calcul:

Suprafaa udat pentru viteza preconizata:

- unde CB este calculat la LWLCoeficientul lui Poisson:

Numrul Reynolds pentru viteza de proiectare:

Coeficientul de rezisten la frecare pentru viteza preconizata:

Coeficientul de influen a rugozitii:

pentru Lpp = 119

EMBED Equation.DSMT4 Coeficientul rezistenei rezidue funcie de :

Coeficientul coreciei datorit raportului

Abaterea LCB (xB) fa de valoarea standard

Coeficient de corecie pentru abaterea centrului de caren:

Corecii pentru bulb n funcie de Fr:

Corecii pentru forma corpului la extremiti:

Coeficientul total al rezistenei rezidue:

Coeficientul total al rezistenei de frecare pentru viteza preconizata:

Corecie datorat rezistenei aerului:

Corecie datorat manevrabilitii:

Coeficientul rezistentei totale:

Rezistena total la naintare a navei pentru viteza de proiectare:

Rezistena i puterea efectiv calculate folosind diagramele, corespund unei nave n condiii de prob, adic pentru condiii ideale privind valurile i vntul, adncimea apei i rugozitatea corpului. Pentru condiii de exploatare se fac o serie de majorari.

Creterile pentru condiii de exploatare se fac asupra rezistenei calculate sau a puterii calculate in funcie de zonele de navigaie a navei. Astfel majorm rezistena la naintare cu 20%. Deci rezistenta la inaintare finala a navei pentru viteza de proiectare va fi:

Rezistena final la naintare a navei

7.2 ESTIMAREA PRELIMINAR A PROPULSIEI I ALEGEREA MOTORULUI

Determinarea preliminar a puterii de propulsie folosind diagramele KT-J :

Din diagrama KT-J n funcie de se extrage valoarea corespunzatoare lui J - obinem J = 0,46

Turaia optim se calculeaz cu relaia :

Se intr n diagrama KT - J cu valoarea obinut pentru kn i se extrage J=0,42Diametrul optim devine :

Din diagrama KT -J se extrage randamentul efectiv .

Vom alege un motor MITSUBISHI tip UEC45LAP1 din catalog cu urmatoarele caracteristici:

putere la flan de 3530 kW

n=158 RPMnumr cilindri 4consum specific 170g/kWh

Lungime 4625 mm

Lime 2560 mm

nlime 7720 mm

Masa 111 t

7.3 PROIECTAREA ELICEI

Tabelul rezistenei la naintare pe o gam de 5 vitezev [Nd]1314151617

v [m/s]6.6887.2027.7178.2318.746

R [kN]194.940271.215284.254319.527393.344

PE1303.7160841953.3482193.4932630.063440.005

w0.3530.3530.3530.3530.353

t0.2610.2610.2610.2610.261

Pentru navele cu o singura elice coeficientul de siaj se calculeaz :

Puterea disponibil la elice este:

Determinarea turaiei optime / diametrului elicei:

turaie motor mic

turaie motor mare se adopt

Ne ncadrm n primul caz n=158 rot/min = 2,63 rot/s. Aadar se calculeaz:

cu acesta intrm n grafice i scoatem un Jopt = 0,46

Tipul de diagram folosit :

KQ-J ; B4-40; z = 4; AE/A0 = 0,4

Calculul se va face tabelar pentru o gam de viteze apropiate de viteza de proiectare.Nr.DenumireSimbolUMViteze

m/s6.697.207.728.238.75

Nd1314151617

1Viteza avans n eliceva=v(1-w)m/s4.3244.6574.9905.3225.655

2Avans relativJ=va/nD-0.370.400.430.460.49

3Raport pasH/D din diagr kQ-J-0.590.610.620.650.68

4Randament elice0 din diagr kQ-J-0.530.550.580.60.62

5Coeficient mpingerekT din diagr KT-J-0.130.1250.120.1250.13

6mpingerea eliceiT=kT*ro*D^4*n^2KN352.670339.105325.541339.105352.670

7Coeficient de influen al corpuluih =(1-t)/(1-w)-1.1431.1431.1431.1431.143

8Randament relativ de rotaier =1,7-CB-0.930.930.930.930.93

9Randament cvasipropulsivD =0*h*r-0.560.590.620.640.66

10Puterea efectiv de remorcarePE=R*v-1086.431627.791827.912191.722866.67

11Puterea disponibilPD=R/D-1924.432778.502958.713429.324340.72

Se vor face dou grafice, unul PD = f(v), si unul H/D = f(v), din care se va extrage o vitez optim pentur puterea disponibil la elice, iar n funcie de aceast vitez un raport de pas corespunztor.

Verificarea la cavitaie

Din diagrama Schonner .

, unde l-am extras din tabele pentru .t0510152030

pd [ N/m2 ]8341226170723354248

Deci elicea nu caviteaz

Geometria elicei, geometria unui profil.

r/Rrx1br=Dx1/zx2bri=brx2bre=br-brix3cr=brx3x4er=Dx4bri-crbre-cr

0.20.3851.6620.6400.6170.3950.2450.350.2240.03660.1410.171-0.030

0.30.57751.8820.7250.6130.4440.2800.350.2540.03240.1250.191-0.066

0.40.772.050.7890.6010.4740.3150.350.2760.02820.1090.198-0.090

0.50.96252.1520.8290.5860.4860.3430.350.2900.0240.0920.196-0.103

0.61.1552.1870.8420.5610.4720.3700.3890.3280.01980.0760.145-0.069

0.71.34752.1440.8250.5240.4330.3930.4430.3660.01560.0600.067-0.007

0.81.541.980.7620.4630.3530.4090.4790.3650.01140.044-0.0120.056

0.91.73251.5820.6090.3510.2140.3950.50.3050.00720.028-0.0910.118

11.925--0----0.0030.012-0.1700.170

Pozititia ordonatei masurata in procenteDiametrul de racordare la muchia de intrare si iesire, in % din grosimea maxima

r/RDe la grosimea maxima la muchia de iesireDe la grosimea maxima la muchia de intrare

10080604020204060809095100r/RMuchia de iesireMuchia de intrare

Ordonatele dosului palei0.255.3572.6586.9096.4598.6094.5087.0074.4064.3556.950.26.4

0.350.9571.6086.8096.8098.4094.0085.8072.5062.6554.900.36.5

0.447.7070.2586.5597.0098.2093.2584.3070.4060.1552.200.46.6

0.543.4068.4086.1096.9598.1092.4082.3067.7056.8048.600.56.7

0.640.2067.1585.4096.8098.1091.2579.3563.6052.2043.350.66.8

0.739.4066.9084.9096.6597.6088.8074.9057.0044.2035.000.76.9

0.840.9567.8085.3096.7097.0085.3068.7048.2534.5525.450.87

0.945.1570.0087.0097.0097.0087.0070.0045.1530.1022.000.911.111.1

Ordonatele fetei palei0.230.0018.2010.905.451.550.452.305.9013.4520.3026.2040.000.9515.715.7

0.325.3512.205.801.700.051.304.6010.8516.5522.2037.55vrf26.7

0.417.856.201.500.302.657.8012.5017.9034.50

0.59.701.750.704.308.4513.3030.40

0.65.100.804.458.4024.50

0.70.402.4516.05

0.80.70

Vrachier 8000 TDW

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